This consistency implies that a valid signaling commitment should ensure that every follower's expected posterior belief is the same, as the leader can only commit to one mixed strategy. We denote by \(\Pi \subset \left(\Delta (\Xi )\right)^K\)  the set of probability measures that are consistent. Finally, we point out that the \(\pi \)  and \(\sigma \)  are equivalent, and the two will be used interchangeablyThe equivalence has been shown in [1]}, and the notion similar to the consistency defined in this paper is referred to as bayesian plausibility in the bayesian persuasion literature [1]}.
